I've been able to mesh a single sphere with an excised sphere (which is essentially just a hollow sphere) by cutting my volume into 8 octants. I can also use the Subtract boolean to remove two spheres from a larger single sphere, however I have been unable to mesh this. I would prefer to use the Sweep meshing scheme.

Here is a typical example of a domain which will need to be meshed. I tried using plane cuts through both excised spheres in all 3 dimensions (leaving 12 regions), but the regions between the excised spheres wouldn't mesh for me.

The journal file below shows one way to mesh your sphere with the 2 sphere cut-outs. You can change the aprepro variables at the top of the journal file to specify a smaller/larger size as fits your analysis needs.